The Ulcer Index

Over the last few issues, we have introduced various risk-adjusted return measures in the Fundamental Focus column. As we have discussed in these columns, most risk-adjusted measures rely on standard deviation as the measure of volatility, or risk. One flaw with using standard deviation is that it accounts for both upside and downside volatility, treating them equally. However, if you are a long-only investor, you are not concerned with upside volatility. In fact, you desire it.

Furthermore, standard deviation is not impacted by the sequence of gains and losses. Therefore, it ignores a string of losses that result in significant drawdowns in your investment’s value. Drawdown is the percentage by which an individual security, portfolio or strategy is down from its all-time high or highest level over a specific period.

In this segment of Technically Speaking, we look at an indicator that measures volatility, but only in the downward direction: the Ulcer Index.

The Ulcer Index was devised in 1987 by Peter G. Martin and Byron McCann. They discussed it in their 1989 book “The Investor’s Guide to Fidelity Funds” (John Wiley & Sons). The index was initially designed to analyze and compare mutual funds, which is why it is only concerned with downside risk—funds are designed to make money by increasing in value over time. Therefore, the only risk is the drawdown, or downside risk.

Calculation

The Ulcer Index is based on a look-back period composed of N periods. As we move from the oldest data to the newest, a highest point is established and maintained and any close below that high is a retracement expressed as a percentage:

Where:

Price is the security price or portfolio value at period i and

MaxPrice is the highest price of the security or highest value of the portfolio to that point in the look-back period.

R1 is always zero—there is no drawdown from the initial price, as it is the high price to that point.

As an example, let’s say we bought a security where on day i the high price to that point is $100 but the price on day i is $95. Therefore, the retracement on day i in this example is –5%.

The Ulcer Index is the quadratic mean (root mean square) of all R (retracement) values, similar to standard deviation:

Where:

R is the retracement value for each period in the look-back period and

N is the number of periods in the look-back period.

As long as the security or portfolio keeps hitting new highs, the Ulcer Index will be zero, meaning there is no downside risk. This is because there is no retracement as long as prices keep going up. Eventually, however, prices are likely to fall and the Ulcer Index will rise above zero.

Interpretation

To plot the Ulcer Index for individual securities, StockCharts.com offers the indicator (www.stockcharts.com). Figure 1 is a two-year weekly price chart for Apple Inc. (AAPL), along with a 14-period Ulcer Index and 14-period standard deviation. Between December 2011 and March 2012, Apple was hitting new highs on almost a weekly basis. As a result, the Ulcer Index dropped steadily throughout this period. However, because of the strong price movement, the standard deviation rose significantly as well. An investor, however, would be happy with this increase in volatility since the price is rising.

After reaching a high in mid-September 2012, AAPL shares began a steady decline until they bottomed out in mid-April of this year. The Ulcer Index rose between September and December 2012, as the shares consistently closed below the 14-period maximum closing price. November’s price rebound reversed the upward trend in the Ulcer Index.

Comparing Investments

Investors can use the Ulcer Index to determine the relative risk of different investments or portfolios, again using StockCharts.com.

Figure 2 shows a weekly line chart plotting closing prices for the Vanguard European Stock Index Fund (VEURX) over the last five years, while Figure 3 is an identical chart for the Vanguard Specialized Portfolios Health Care Fund (VGHCX). Both charts also plot the 14-week Ulcer Index (the thick black line) under the price chart as well as a 52-week moving average of the Ulcer Index (the more smooth thin blue line) that serves to smooth the index as well as show a long-term average.

Looking at Figure 2, we see that the Ulcer Index rose above 15 on three occasions. The 2008–2009 financial crisis drove down the value of most investments, so it is not surprising that would we see a spike in the Ulcer Index during that period. Since then, the Ulcer Index for VEURX has risen above 15 only once, in late September 2012, and for only a few weeks. The 52-week simple moving average of the Ulcer Index for VEURX shares is 3.2.

Referring to Figure 3, VGHCX shares have seen an Ulcer Index above 15 only once, also during the 2008–2009 market downturn. Furthermore, the 52-week moving average is 1.2, which is significantly lower than that of VEURX shares. The health care fund has less drawdown potential, or downside risk, than the European fund.

Conclusion

Investors can use the Ulcer Index to measure the downside risk, or drawdown potential, of a security or a portfolio. For long-only investors, this is the risk of most concern. An Ulcer Index near zero means prices are regularly hitting new highs, while a rising index indicates that prices are closing below recent highs.

You can also use the Ulcer Index to calculate risk-adjusted returns. The Spreadsheet Corner article in this issue expands on this theme using AAII’s stock screens.

Discussion

Mark Day from VA posted over 3 years ago:

excellent article and new tool. the measurement of volatility without regard to whether its positive or negative is a critical weakness of traditional approach. This corrects for this key error. Indeed it would be great to have the companion to ulcer index - the "pleasure index" of volatility to the upside.

Frederic Van Paten from NY posted over 2 years ago:

I have printed the calculating a Firm's Cash Burn Rate because I'm learning from your article's. I also printed Support and Resistance Levels and Stochastic Oscillator.